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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

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Equilateral Areas

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

Inscribed in a Circle

Age 14 to 16 Challenge Level:

The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.

What is the area of a regular hexagon inscribed in a circle with a unit radius?

 

What is the area of an equilateral triangle inscribed in a circle with a unit radius?